Finite Group DatabasebetaFinite Group Databasebeta| order | 3468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #13181892⋊C2 |
| unambiguous semidirect product | ((C17⋊D17)⋊C3)⋊C2 |
| Fitting, socle, Sylow | C172 ⋊ C2×D3 |
| derived, Hall | C172⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C172⋊C3 | C22 |
| Fitting, socle | C172 | C2×D3 |
| LCS | G ▷ C172⋊C3 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 51 |
Polycyclic presentation:
2^2,3,17^2|c^a=c^2,d^a=d^14e^5,e^a=d^12e^3,c^b=c^2,d^b=d^3e^12,e^b=d^5e^14,d^c=d^14e^5,e^c=d^2e^254 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3468, 23);